Why time limit difference between IDEone.com and SPOJ?

You might have used few test cases only. Try to run your code for extreme cases ( max no. of test cases ). Also be specific about the problem which you are solving.

I'm new to programming, so I don't know much about optimization. My code for problem PRIME1 exceeded time limit. Is it possible to optimize the code enough or is the algorithm itself too slow?

#include <iostream>
#include <string>
#include <stdlib.h>
using namespace std;
int main() {
	int times;
	cin >> times;
	int *nums = new int[times*2];
	string temp;
	for (int t = 0; t < times*2; t+=2) {
		getline(cin, temp, ' ');
		nums[t] = atoi(temp.c_str());
		getline(cin, temp);
		nums[t+1] = atoi(temp.c_str());
	}
	bool prime = false;
	for (int t = 0; t < times*2; t+=2) {
		for (int i = nums[t]; i <= nums[t+1]; ++i) {
			if (i > 1) prime = true;
			for (int j = 2; j < i; ++j) {
				if (i % j == 0) {
					prime = false;
					break;
				}
			}
			if (prime) cout << i << endl;
		}
		cout << endl;
	}
	return 0;
}

I hope somebody can give me some suggestions.

Thanks in advance!

Try the Sieve of Eratosthenes algorithm:
en.wikipedia.org/wiki/Sieve_of_Eratosthenes6